2x^2=11x+21

Solution for 2x^2=11x+21 equation:

Simplifying
2x2 = 11x + 21

Reorder the terms:
2x2 = 21 + 11x

Solving
2x2 = 21 + 11x

Solving for variable 'x'.

Reorder the terms:
-21 + -11x + 2x2 = 21 + 11x + -21 + -11x

Reorder the terms:
-21 + -11x + 2x2 = 21 + -21 + 11x + -11x

Combine like terms: 21 + -21 = 0
-21 + -11x + 2x2 = 0 + 11x + -11x
-21 + -11x + 2x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
-21 + -11x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1.5, 7}